Question 499299: How many cups of grapefruit juice must be added to 40 cups of a punch that is 2% grapefruit juice to obtain a punch that is 10% grapefruit juice?
Answer by oberobic(2304)   (Show Source):
You can put this solution on YOUR website! To solve mixture problems, you have to determine how much "pure" stuff you have and how much you need in the final mix.
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You have 40 cups of 2% grapefruit juice.
40*.02 = .8 cup of pure grapefruit juice, or 8/10 of a cup.
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You have an unlimited supply of 100% grapefruit juice that you have to mix with the 2% to obtain a final amount of juice mixture that is 10% grapefruit juice.
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Looking at this logically, if you had 10% juice, you would have to have 4 cups of pure juice in the 40 cups of punch. But, everything you add increases the volume, so you have to model it.
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x = amount of pure juice to add
40+x = amount of 10% punch you will have in the end.
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Pure grapefruit juice in the final produce = 10%*(40+x).
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Your ingredients are:
2%*40 + 100%*x = 10%*(40+x)
.02*40 + x = .1(40+x)
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Multiply by 100 to remove percents
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2*40 + 100x = 10(40+x)
80 + 100x = 400 + 10x
90x = 320
x = 320/90
x = 32/9 cups
x = 3 5/9 cups to add to the 40 cups you have
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Check your answer by determining how much pure stuff you have vs. how much you ought to have.
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You have 43 5/9 cups of total mix.
= 43.555 cups
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You have 8/10 + 32/9 cups of pure stuff.
= 4.3555 cups
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So, the final mixture is indeed 10% grapefruit juice.
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Answer:
Add 3 5/9 cups of pure grapefruit juice.
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